Cameras with the clean feature do so on startup and shutdown, so prompting it to do this probably wouldnt make any difference.
Bare in mind that when you blow it with a rocket blower you need to (as suggested above) have the camera facing down (for the dirt to fall out, and no more to fall in) You also need to use manual clean (this is a feature in the cleaning menu) to flip the mirror up to reveal the sensor otherwise your only blowing dust off the mirror.
A proper clean is the best solution. Find a friend that can do it if you want to save cash.
One note, its important to have a well charged battery in the camera if your going to manually clean or get anything inside the camera. If the mirror flips down as the battery has run out it will knacker your camera. Modern Canon's wont actually allow you to clean if the battery is much below 50%, but i have no idea if this is the same for Nikon.
The swab size depends on the sensor size - e.g 1.5x 1.6 etc.. Ideally the swab is the exact height of the sensor.